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Chapter 2: Problem 50

When do we say that a pendulum has completed one oscillation?

Short Answer

Expert verified
Answer: A pendulum completes one full oscillation when it has moved from its initial displacement (maximal displacement from the equilibrium position) through its equilibrium position to the maximal displacement on the other side, and then back to its initial displacement.

Step by step solution

01

Understand the concept of a pendulum

A pendulum is a simple mechanical device consisting of a weight (bob) attached to a string or rod, which is allowed to swing back and forth under the force of gravity. When the bob is displaced from its equilibrium position, it experiences a restoring force that returns it back to the equilibrium position. The pendulum follows a periodic motion, that is, it repeats the same motion over and over again.
02

Identify the equilibrium position

The equilibrium position of the pendulum is the point where the bob, when not experiencing any external forces, will come to rest. In a pendulum, this position occurs when the bob is hanging straight down, and the string (or rod) is vertical.
03

Determine the starting point and finishing point of a single oscillation

To initiate the oscillation, the pendulum must be displaced from its equilibrium position and released. The bob will then swing back and forth from one side to the other and eventually return to its starting point. A pendulum completes one full oscillation when it swings from its starting point, reaches the opposite extreme, and then returns to its original position.
04

Explain when a pendulum has completed one oscillation

A pendulum has completed one full oscillation when it has moved from its initial displacement (maximal displacement from the equilibrium position) through its equilibrium position to the maximal displacement on the other side, and then back to its initial displacement. This complete motion comprises one full oscillation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Pendulum Motion
The fascinating journey of a pendulum starts with a simple yet powerful principle. A pendulum consists of a weight, often called a bob, suspended from a string or rod, that swings back and forth under the influence of gravity.
This swinging action is known as pendulum motion. When the pendulum bob is pulled to one side and then released, it is displaced from its resting, or equilibrium, position.
The fascinating aspect of pendulum motion is that it is predictable and consistent. It moves through the same path, back and forth, repeatedly, which is affected by factors such as the length of the string and gravity. Here鈥檚 a quick rundown of pendulum motion:
  • It is initiated when the bob is displaced from rest.
  • The pendulum swings to an extreme position, then to the opposite side, and returns to its starting point.
  • This back-and-forth movement is predictable and is used in clocks and scientific instruments.
Equilibrium Position
The equilibrium position is a critical concept in pendulum dynamics. This is the position where the bob naturally comes to rest when no additional forces act upon it.
In a pendulum, the equilibrium position is when the bob hangs directly below its pivot point. Here, the string is perfectly vertical, and the forces on the bob are balanced. To visualize this better:
  • Imagine the pendulum at rest, with no movement - this is the equilibrium position.
  • If displaced from this spot, the bob experiences a restoring force due to gravity.
  • The restoring force attempts to pull the bob back to this equilibrium position.
Understanding the equilibrium position helps in predicting how the pendulum will behave when set in motion.
Periodic Motion
Periodic motion is a wonderful property of pendulums that describes how their movements repeat after regular intervals. A pendulum is considered in periodic motion because each swing takes the same time to complete, no matter the overall swing amplitude, given small oscillations.
This type of motion is not only predictable but also very important in technological applications. For instance:
  • Every swing from one extreme to the other and back is called an oscillation.
  • The time it takes to complete one oscillation is called the period.
  • Clocks, which use pendulums, rely on this periodic nature to keep accurate time.
The regularity of this motion is key, allowing pendulums to be precise tools in timing and measurement.

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Most popular questions from this chapter

In a \(100 \mathrm{~m}\) race, 'A' touches the finishing line in \(10.5\) second and 'B' touches it in 11 second. Who is faster, 'A' or 'B'?

In a race, two athletes 'A' and 'B' reach the finishing point in 20 second and 22 second respectively. (a) What is the ratio of their speeds? (b) If both are allowed to run with their respective speeds for a given time, what is the ratio of the distance covered by them?

The time taken by the bob of a simple pendulum of time period \((\mathrm{T})\) to move from one extreme position to other extreme position is equal to _

The time period of a pendulum is independent of (1) length of the pendulum (2) mass of the bob (3) shape of the bob (4) Both (2) and (3)

What is meant by average speed? How is it calculated?
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